In: Statistics and Probability
(12 pts.) A new diet has been developed for raising beef cows. Two random samples of size fifteen are independently selected, and one is given the new diet and the other is given the standard
diet. After 18 weeks, the weight gain was measured, and it was found that x1 = 35 with s1 = 8 and x2 = 26 with s2 = 6. Let μ1 and μ2 represent the mean weight gain we would observe for the entire
population of beef cows when on, respectively, a new diet and a standard diet. Assume that two- sample t procedures are safe to use.
(a) Test the following hypotheses using α=0.05 :
Ho:μ1=μ2,Ha:μ1>μ2
(b) Calculate 95% confidence interval for μ1 – μ2